Ivan and kate live 42 miles apart. ivan leaves his house at 8:00 a.m. and bikes towards kate's house at a constant speed of 12 m
1 answer:
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<span>ACF is a 30º-60º-90º triangle because of the following:
</span>1) Based on a theorem, in a 30°-60°-90° triangle the sides are in the ratio 1 : 2 : √3<span>
1 </span>→ short leg
2 → hypotenuse
√3 → long leg
<span>
Side length of the hexagon is the short leg of the triangle. It is 1.
r1 is the radius of the incircle in a regular hexagon. 2(r1) is the diameter of the incircle. It is also the hypotenuse of the right triangle. It is 2.
</span><span>Using Pythagorean theorem.
</span>a² + b² = c²
1² + b² = 2²
b² = 2² - 1²
b² = 4 - 1
b² = 3
√b² = √3
b = √3
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</span>
<span>
</span>
<span>
</span>
</span>1) Based on a theorem, in a 30°-60°-90° triangle the sides are in the ratio 1 : 2 : √3<span>
1 </span>→ short leg
2 → hypotenuse
√3 → long leg
<span>
Side length of the hexagon is the short leg of the triangle. It is 1.
r1 is the radius of the incircle in a regular hexagon. 2(r1) is the diameter of the incircle. It is also the hypotenuse of the right triangle. It is 2.
</span><span>Using Pythagorean theorem.
</span>a² + b² = c²
1² + b² = 2²
b² = 2² - 1²
b² = 4 - 1
b² = 3
√b² = √3
b = √3
<span>
</span>
<span>
</span>
<span>
</span>
Answer:
Option 4 - 53
Step-by-step explanation:
Given : Lydia runs an experiment to determine if a coin is fair by counting the number of times a coin lands heads up. The table shows her data.
To find : According to the line of best fit, about how many times would the coin land heads up in 100 flips?
Solution :
We create the table of coin fairness table
Number of coin flips - 0 10 20 30 40 50 60 70 80 90
Number of heads up - 0 7 12 18 23 30 35 38 42 45
Now, using linear regression calculator,
We get the best line fit for the data
i.e,
Now, for heads up in 100 flips we substitute x=100
Graphically we plot the equation and see the point at x=100
The point is (100,52.935)
Or approximately the coin land heads up in 100 flips is 53.
Therefore, Option 4 is correct.
Refer the attached figure.
